"...If a cell is empty, there may be no turn in that cell..."
Shouldn't this be
"...If a cell is empty, there cannot be a turn in that cell..." ?
Otherwise what is the difference between that and a cell with a diamond?
I didn't notice it myself, but you are correct: the word was an unlucky choice. My suggestion: "If a cell is empty, the path cannot turn in that cell".
Or "can't", whichever suits you better.